Input/Output Characteristics and Errors
Gage Interconnection Configurations
Strain gages have been used for many decades for measuring the stresses in mechanical components of aircraft and other active and passive structures.
Sometimes, one simple gage can give the necessary information, and in those instances where hundreds or even thousands of gages are needed to implement a large test, use of the quarter bridge configuration of Figure 34 is a cost control necessity. The only active bridge leg (a strain gage) is shown as (AC), and the other three inactive legs (A'B', B'D' and C'D') are fixed resistors, to simulate a complete bridge.
Figure 34. Quarter bridge connection
Figure 35. Half bridge connection
Figure 36. Full bridge connection
In certain cases, it is even possible to use the quarter bridge in a load cell, where temperature compensation and moment compensation are not a necessity, as in a cheap bathroom scale.
The half bridge connection is usually used for low cost load cells which are designed for specific OEM applications, where the customer can adapt a special design to make use of the cell’s unique parameters.
The full bridge is the only one which has enough active legs to allow for easy compensation for temperature coefficients of both zero and span and to allow adjustment of moment sensitivity.
Other parameters being equal, a full bridge has twice the output of a half bridge and four times the output of a quarter bridge.
Temperature Effect on Zero and Output
Interface proprietary gages are designed specifically to compensate the temperature effect on the modulus of elasticity of the flexure material, thus providing essentially a constant output over the compensated temperature range. The specification for each load cell series states the coefficient, typically ±0.08% per 100 degrees F.
Temperature compensation, zero balance
A small zero balance shift, due to the differences between the temperature coefficient of resistance of the gages, must be tested and adjusted at the factory.
The usual method in the load cell industry uses only two temperatures, ambient room and 135°F. The best result which can be obtained by this method is shown in Figure 37 as the “room-high compensated” curve.
At Interface, the test is run at both low and high temperature. This method is more costly and time consuming, but it results in the “c-h compensated” curve, which has two distinct advantages.
- The curve’s maximum occurs near room temperature. Thus, the slope is almost flat over the most-used temperatures near room ambient.
- The overall variation over the compensated temperature range is much less.
Figure 38. Temperature effect on output
Figure 39. Temperature effect on zero
The graphs of Figures 38 and 39 show, separately, the effect of temperature on zero balance and output, so it is easier for the reader to visualize what happens to the signal output curve of the load cell as the temperature is varied. Notice that zero shift moves the whole curve parallel to itself: while output shift tips the slope of the output curve.
Load Cell Electrical Output Errors
Figure 40. Simplified error graph
When a load cell is first calibrated, it is exercised three times to at least its rated capacity, to erase all history of previous temperature cycles and mechanical stresses. Then, loads are applied at several points from zero to rated capacity. The typical production test for a Low Profile cell consists of five ascending points and one descending point, called the “hysteresis point” because hysteresis is determined by noting the difference between the outputs at the ascending point and corresponding descending point, as shown in Figure 40. Hysteresis is usually tested at 40 to 50 percent of full scale, the maximum load in the test cycle.
Figure 41. Static error band
There are many definitions of “best fit straight line,” depending on the reason that a linear representation of the output curve is needed. The end point line is necessary in order to determine non-linearity, the worst case deviation of the output curve from the straight line connecting the zero load and rated load output points. (See Figure 40.)
A more sophisticated and useful straight line is the SEB Output Line, a zero-based line whose slope is used to determine the Static Error Band (SEB). As shown in Figure 41, the static error band contains all the points, both ascending and descending, in the test cycle. The upper and lower limits of the SEB are two parallel lines at an equal distance above and below the SEB Output Line.
The reader should keep in mind that the non-linearity, hysteresis and nonreturn to zero errors are grossly exaggerated in the graphs to demonstrate them visually. In reality, they are about the width of the graph lines.
Resistance to Extraneous Loads
All load cells have a measurable response when loaded on the primary axis. They also have a predictable response when a load is applied at an angle from the primary axis. (See Figures 42 and 43.) The curve represents the equation:
Figure 43. Relative output versus angle
Figure 42. Off-axis loading
For very small angles, such as the misalignment of a fixture, the cosine can be looked up in a table and will be found to be quite close to 1.00000. For example, the cosine of 1/2 degree is 0.99996, which means the error would be 0.004%. For 1 degree, the error would be 0.015%, and for 2 degrees, the error would be 0.061%. In many applications, this level of error is quite livable. For large angles, it would be advisable to calculate the moment induced in the cell, to ensure that an overload condition will not occur.
Figure 44. Extraneous load vectors
Because of the close tolerance machining of flexures, the matching of gages; and precision assembly methods, all Interface load cells are relatively insensitive to the extraneous loads shown in Figure 44: moments (Mx and My), torques (T), and side loads (S). In addition, the resistance to extraneous loads of the Low Profile Series is augmented by an additional step in the manufacturing process which adjusts the moment sensitivity to a tighter specification.
Take care not to exceed the torque allowances in the specifications. The torque figures for attaching fixtures to a load cell are much less than the Mechanics Handbook values for the same sized threads.
Customers frequently ask, “What are the resolution, repeatability, and reproducibility of Interface load cells?” The answer is, “Those are system parameters, not load cell parameters, which depend on (1) the proper application of the load cell, (2) the forcing systems and mechanical fixtures used to apply the loads, and (3) the electrical equipment used to measure the load cell output.”
Load cell resolution is essentially infinite. That is to say, if the user is willing to spend enough money to build a temperature-stable, force-free environment and to provide extremely stable, high gain electronics, the load cell can measure extremely small increments of force. The most difficult problems to solve are temperature variations from heating/cooling systems, forces such as air motion and building vibration, and the inability of hydraulic forcing systems to maintain a stable pressure over time. It is very common for users to demand, pay for, and get too much resolution in the measuring equipment. The result is outputs which are difficult to read, because the display digits are continually rolling due to instabilities in the overall system.
Non-repeatability is frequently blamed on the load cell, until the user takes the trouble to analyze and track down all the causes of so-called “erratic” readings. Under optimum mechanical and electrical conditions, repeatability of the load cell itself can be demonstrated to be at the same order of magnitude as resolution, far better than necessary in any practical force measurement system.
Repeatability is affected by any one of the following factors:
- Tightness of the mechanical connection of fixtures
- Rigidity of the load frame or force application system
- Repeatability of the hydraulic forcing system itself
- Application of a dead weight load too quickly, causing over-application of the force due to impact
- Poor control of reading times, introducing creep into the data
- Unstable electronics due to temperature drift, power line susceptibility, noise, etc.
Reproducibility is the ability to take measurements on one test setup and then repeat them on different test setup. The two setups are defined as different if one or more element in the setup is changed. Therefore, inability to repeat a set of measurements could be found in one facility where only one fixture was changed. Or, a discrepancy could be uncovered between two test facilities, which could become a major problem until the differences between the two are analyzed and corrected.
Reproducibility is a term not heard very often, but it is the very essence of the calibration process, where a cell is calibrated at one location and then used to measure forces at another location.
Reproducibility is achieved most easily by using Interface Gold Standard® load cells. The low moment sensitivity makes them less susceptible to misalignments in load frames. That, combined with the permanently installed loading stud, high output, and low creep, make them the cell of choice with users who cannot compromise – who need the very best.